The key piece of information here is that your speakers are very insensitive and they are very difficult to drive. One of the first questions you must answer is how loud you like to listen and how big and dead is your room. These are bookshelf speakers so one might expect that you would play them at moderate volumes but If you like to listen at high volumes and if your room is large with a carpeted floor and lots of furniture you are going to need an amp with high wattage that doubles its power into 4 ohms and preferable doubles its power again into 2 ohms.
I suggest that you consider the amp's ability to put out substantial power at 2 ohms as one of your main criteria. If the manufacturer doesn't list power output at 2 ohms then IMO you should rule it out.
Here is an example of an integrated amp that you can find on the used market that has a very high current output - Denon PMA 2000IVR. It's rated at 80 watts into 8 ohms and 320 watts into 2 ohms. I have one of these in my secondary system and it sounds very good. There are several iterations of this amp but the series all has the beefy power output. They cost between $500 and $1000 for one in mint condition. This amp would be a good baseline and later on when you want to upgrade it would be an excellent reference.
If you go out and spend a bunch of money on a new amp it's going to be impossible to make a judgement of its sound because you have nothing to compare it to. You might think it doesn't sound very good but your problem could be any number of things besides the amp. Going with a competent used amp to start with will allow you to optimize your system regarding speaker placement, room acoustics, and maybe the addition of a subwoofer. Then when you get the bug to upgrade you have the ability to hear whether or not it sounds better.
I suggest that you consider the amp's ability to put out substantial power at 2 ohms as one of your main criteria. If the manufacturer doesn't list power output at 2 ohms then IMO you should rule it out.
Here is an example of an integrated amp that you can find on the used market that has a very high current output - Denon PMA 2000IVR. It's rated at 80 watts into 8 ohms and 320 watts into 2 ohms. I have one of these in my secondary system and it sounds very good. There are several iterations of this amp but the series all has the beefy power output. They cost between $500 and $1000 for one in mint condition. This amp would be a good baseline and later on when you want to upgrade it would be an excellent reference.
If you go out and spend a bunch of money on a new amp it's going to be impossible to make a judgement of its sound because you have nothing to compare it to. You might think it doesn't sound very good but your problem could be any number of things besides the amp. Going with a competent used amp to start with will allow you to optimize your system regarding speaker placement, room acoustics, and maybe the addition of a subwoofer. Then when you get the bug to upgrade you have the ability to hear whether or not it sounds better.